Why do you think the ACP is right wing and reject Marxism? Literally they mention being Marxist-Leninist multiple times on the website you link. Nothing I’ve ever heard them espouse has been right wing, but I’d love if you could point me to some analysis that explains how you arrived at that conclusion.
The ACP is a group of PatSocs, also known as MAGA Communism. They advocate for Patriotism and Nationalism within the Imperial Core, as opposed to an emphasis on Internationalism, which means it is opportunist and revisionist at minimum and plays into the hands of Imperialists. Ie, PatSocs side with the Imperialist Capitalists of their own country and advocate for central planning and other “Marxist” ideas.
They are similar to the German Nazi Party but with more lip service to Marxism.
This is not to be confused with the Communist Party of the USA, which is Reformist and thus Revisionist.